A nonzero-sum game approach to convertible bonds: Tax benefit, bankruptcy cost, and early/late calls

Abstract

Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. The conflicts of interest between bondholders and shareholders affect the security prices significantly. In this paper, we investigate how to use a nonzero-sum game framework to model the interaction between bondholders and shareholders and to evaluate the bond accordingly. Mathematically, this problem can be reduced to a system of variational inequalities and we explicitly derive the Nash equilibrium to the game. Our model shows that credit risk and tax benefit have considerable impacts on the optimal strategies of both parties. The shareholder may issue a call when the debt is in-the-money or out-of-the-money. This is consistent with the empirical findings of "late and early calls." In addition, the optimal call policy under our model offers an explanation for certain stylized patterns related to the returns of company assets and stocks on call. © 2012 Wiley Periodicals, Inc.